[American Institute of Aeronautics and Astronautics 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference - St. Louis, Missouri (24 June 2002 - 26 June 2002)] 8th AIAA/ASME

AIAA 2002-3222

American Institute of Aeronautics and Astronautics

1

SPECTRAL OPTICAL PROPERTIES OF NONEQUILIBRIUM HYDROGEN PLASMA FOR RADIATION HEAT TRANSFER

S. SurzhikovInstitute for Problems in Mechanics Russian Academy of Sciences

prosp. Vernadskogo 101, Moscow, 117526, RussiaM. Capitelli, G. Colonna

Centro di Studio per la Chimica dei Plasmi del CNR, Dipartimento di Chimica, Universita di Bari,via Orabona 4, 70126 Bari, Italy

Abstract

Quasiclassical theory of spectral optical properties of two-temperature hydrogen plasma is presented. Spectral absorption coefficients of two-temperature hydrogen plasma are calculated and presented for temperatures of heavy particles T = 5000÷20000 K and electronic temperatures Te = 5000÷40000 K.

Introduction*

Study of radiation heat transfer in nonequilibrium gases and plasma is one of urgent tasks of the modern physical-chemical mechanics in the various aerospace applications. The fundamental basis of the radiation processes theory and calculations is the spectral absorption (emission) coefficient of the radiation.

The spectral absorption (emission) coefficient is comprised of two factors. There are: the population of the absorbing species and the cross-section per particle (the absorption coefficient per one particle). The first of these factors is obtainable from the statistical physics, and a full discussion as well as tables of hydrogen particles population are given for the two-temperature hydrogen plasma in Ref.1. The second of these factors requires a quantum mechanical description of atomic and molecular structure to determine radiative transition probabilities. But for some plasma conditions which are of practical interest for aerospace applications the radiative transition probabilities can be predicted by a quasiclassical theory. This theory is based on the Kramers [2] and Unsold [3] quasiclassical approach, and is discussed for the case of the two-temperature plasma in the given paper. Developed theory is used for calculation of the two-temperature hydrogen plasma in wide region of temperatures of heavy particles and electrons.

The initial data for the quasiclassical theory are the volumetric concentration of particles of hydrogen plasma

* Corresponding author: professor Surzhikov S.T., Institute for Problems in Mechanics RAS, Moscow, 119526, Russia. AIAA member. E-mail: [email protected] by the American Institute of Aeronautics and Astronautics. Inc. All rights reserved

( + -2H H H e, , ,N N N N ), and temperature of heavy particles

T and electrons eT .

The following four types of radiating processes will be considered [4,5]:• Brake radiation of electrons in the H+ fields and

"braking" absorption process (continuous absorption at free-free (f-f) quantum transitions);

• Free electrons capture by the H+ ion with an emissivity of light quantum and photo-ionization processes;

• Bound-bound quantum transitions in the H atom with formation of atomic lines in radiation and absorption processes;

• Electronic quantum transitions in the H2 molecule with formation of electron-vibrational bands of absorption and emissivity.Developed theory and calculated data may be

recommended for analysis of radiation heat transfer in nonequilibrium low-temperature hydrogen plasma.

1. Emitting and absorbing radiating processes in the H+

ion Coulomb field

The electromagnetic energy emitted in a spectral range dν in a vicinity of the frequency ν at braking of an unitary flow of electrons on the isolated ion in all range of aiming distances may be estimated by the following formula

2 2 6

2 3 2e e

8 1d d

3

Z eq

m cν

π ν= ⋅v

, (1)

where z is the ion charge multiplicity , e is the electron charge, em is the electron weight, c is the velocity of light,

ev is the velocity of the electrons flow.

8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-3222

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

AIAA 2002-3222


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Approximate Eq.(1) is received in [6] by a simple and evident way. More detailed consideration results in the following formula [7]

2 2 6

2 3 2e e

32 1d d

3 3

Z eq

m cν

π ν= ⋅v

, (2)

which specifies (1) only in a part of numerical coefficient.The classical Eq.(2) is correct at

3e e

22

m

Zeν π>>

v(3)

or

e2

1h

Zeπ <<v(4)

The Eq.(2) will be used as basis of the quasiclassical theory.Let electronic gas is characterized by the Maxwell distribution on speeds with the temperature eT , then:

( )3 2 2

2e e ee e e e

e e

d 4 exp d2 2

m mf

kT kTπ π

= −

vv v v v . (5)

The following normalization of the distribution

function is used: the ( )e e e edf N v v v is the number of

electrons in 1 cm3 with speeds in the following range

( )e e ed÷ +v v v .

If iN is the ions concentration in 1cm3, then

( )i e e e ed dN qν⋅N f v v v

is the energy emitted per 1 s from the volume 1 cm3 by electrons with speeds ev , braked near to these ions with a

charge Z.Then energy which is emitted per 1 s from the volume

1 cm3 by all electrons, which velocity surpasses e∗v is

determined under the following formula

( )e

e i e e ed d dj N qν νν∗

∞= ⋅∫

v

N f v v v , (6)

where e∗v is determined by the following condition

2e e( )

2

mhν

∗=

v,

as at smaller velocity e∗v energy quantum hν will not be

emitted.Substitution (2) into (6) results in

( )e

e

2 2 6

e i e e2 3ee

1 22 6

e i3e ee

32 1d d d

3 3

32 2d .

3 3h kT

Z ej N

m c

Z ee N

m kTm c

ν

ν

πν ν

π π ν

∗

∞

−

= ⋅ =

=

∫v

N f v vv

N

(7)

The Eq.(7) sets spectral radiant emittance (energy radiated in the interval dν from 1 cm3 per 1 s). Let's remind, that the following two assumptions were used:1. The electronic gas has Maxwellian distribution on speeds;2. The approximation of the “high frequencies” is correct, that is

( )3 35 3 2e e e

e2 26.21 10

2 2

m mT

Ze Zeν π π>> = ⋅v

,

where 5e

86.21 10 k

kTT

mπ= = ⋅v cm/s.

In view of numerical meanings of constants which are included in Eq.(7), the spectral radiant emittance can be rewritten

e2

37e i1 2

e

d 0.683 10 dh kTZj e N

Tνν ν ν−−= ⋅ N . (8)

Passing to measurement of spectral dependence in wave numbers, one can receive

d dj jν ων ω= ,

e2

1.43937i e1 2

e

d= 0.683 10

dTZ

j j c e N NT

ωω ννω

−−= ⋅ ⋅ ,

3

ergcm

cm s⋅ (9)

or, taking into account a numerical meaning of a light velocity:

e2

1.43926i e1 2

e

0.205 10 TZj e N N

Tωω −−= ⋅ ,

3

ergcm

cm s⋅ (10)

Group radiant emittance can be obtained by integrating of the Eq.(10) over given spectral group:

dg

gj jωω

ω∆

= =∫e

21.43926

i e1 2e

0.205 10 dg

TZe N N

Tω

ωω−−

∆= ⋅∫ ,

3

ergcm

cm s⋅ (11)

And finally, integrated (total) radiant emittance in the free-free braking processes can be written as follows:

237

1 2e0

d 0.683 10Z

J jT

ν ν∞

−= = ⋅ ×∫e

226 e

e i1 2ee 0

0.205 10 dg

h T kTZ hN N e

kT hTν

ων

∞−−

∆× ⋅ ⋅ =∫ ∫

237

e i e1 2e

0.683 10Z k

N N ThT

−= ⋅ ⋅ (12)

or

26 2 1/ 2e i0.142 10 eJ Z T N N−= ⋅ ,

3

erg

cm s⋅ (13)

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2. Coefficients of the free-free “braking” absorption

The term of the “braking” absorption used here should be understood as process of photons absorption during acceleration of electrons in the Coulomb field of ions.

Let us assume, that the basic source of the electromagnetic energy emissivity and absorptivity for the considered case are the free-free electrons transitions in ion fields. Therefore the intensity of the processes is defined by the electronic temperature. Therefore the principle of the detailed balance can be applied in the following form

( ) ( ) ( )ei e e ed 1 h kT

pN N f cU e νν νκ −− =%v v

( )i e e e ed dN N f qν′ ′ ′= v v v (14)

where: ( )e e edN f v v is the number of electrons in 1 cm3

with speeds ( )e e ed÷ +v v v ; pcUν is the volume density of

the radiative energy; e1 h kTe ν−− is the contribution to the forced radiation.

The left part of Eq.(14) sets quantity of radiant energy, absorbed by electrons with speeds ( )e e ed÷ +v v v per 1 s

in 1 cm3. The right part of Eq.(14) gives quantity of radiant energy emitted at braking of electrons with speeds

( )e e ed′ ′ ′÷ +v v v per 1 s in 1 cm3.

Connection between velocities e eand′v v can be

written in the following form:2 2 2 2

e e e e e e e e,2 2 2 2

m m m mh hν ν′ ′

= + = −v v v v

Or e e e e e ed dm m′ ′ =v v v v (15)

Let's assume that d dq hν νν σ= , (16)

where νσ is the spectral cross-section of the braking

emissivity. The spectral volume density of the Planck radiant

energy can be presented in the form

( )3

3

8 1

exp 1pe

hU

h kTcν

π νν= ⋅ − . (17)

Therefore, taking into account

( )3 2 2

2e e ee e e e

e e

d 4 exp d2 2

m mf

kT kTπ π

= −

vv v v v ,

and relationship 2 2

e e e e e e e2 2h kT m kT m kTe e eν ′− = −v v ,

we shall receive

( )22ee

2e

d

d8

c ννσκ νπν

′′=% vv

v.

Having substituted ( ) ( )e ed dq hν νσ ν′ ′=v v , one can

receive well known Kramers’ formula

2 6

2 3e e

4

3 3

Z e

hcmν

πκ ν=%v

, cm5

The braking absorption coefficient can be received by integration:

2 6

e i2 3e

4

3 3

Z e

hcmν

πκ ν= ×N N

3 2 22e e ee e

e e e0

14 exp d

2 2

m m

kT kTπ π

∞ × − = ∫ v

v vv

1 22 6

i e2 3e ee

4 2

3 3

Z e

m kThcm

πν

=

N N . (18)

Taking into account numerical meanings of the coefficients, one can derive

28

e i1 2e

3.69 10Z

Tνκ ν= ⋅ N N , cm−1 (19)

And finally, in view of the Gaunt factor2

8e i1 2

e

3.69 10Z

gT

νκ ν= ⋅ N N , cm−1

( ) ee e 2 1 3

e

43ln

kTg g N T

e Nπ= = =

e e1

1.27 3.38 lg lg3

T N = + − . (20)

3. Spectral cross-section of an electron capture by ion with emissivity of light quantum

The quasiclassical condition of considered process is analyzed in Ref.6. This condition has the following form

22e e

H2

mI Z<<

v. (21)

For the hydrogen atom 2 10

H 02 13.6 eV 0.218 10 ergI e a −= = = ⋅ .

Estimation of the electrons thermal velocity is: 5

e,6.21 10e kv T= ⋅ , cm/s

Then, the quasiclassical condition can be rewritten in the following form

( )2

e, 25e

2

6.21 10k H

ZT I

m<<

⋅ or 5

e, 1.24 10 KkT << ⋅ (22)

The schematic of the process under consideration is shown in Fig. 1.

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Fig. 1. The schematic of the energy levels and quantum transitions. The levels of energy are counted from border between the discrete and continuous spectrum

Taking into account Fig.1 one can present the following energy balance

2e e

22

m Ih

nν = +

&v, (23)

where n is the number of the energy level for hydrogen-like atom.Let e,nσ is the effective cross-section of the emissivity

from n∆ group of levels, then

e,nq h nν νσ∆ = ∆ .

From here one can find

e,nq

h nνσ ν

∆= ∆ . (24)

Let us substitute qν∆ from Eq.(2) into the Eq.(24), then

2 2 6

e, 2 3 2e e

32 1 d

d3 3n

Z e

h nm c

π νσ ν= ⋅ ⋅v

.

But from Eq.(23) there is the following relation

4 3

2 2d d d d

nI Ih n, n

n hnν ν= =

& &

Therefore2 2 6

e, 3 2 2 3e e e

32 2

3 3n

Z e I

m c h n

πσ ν= ⋅ ⋅ &m v

. (25)

And, taking into account the numerical meanings of the coefficients, one can write

26

e, 2 3e e

2 10.692 10n

IZ

nσ ν

−= ⋅ ⋅ ⋅&m v

, cm2 (26)

The cross-section over all levels can be found by the summation:

6 2e 3

e

10.692 10

n n

IZ h

E n hσ ν∗

∞−=

= ⋅ ∑&,

where 2

e ee 2

E =m v

.

Taking into account Eq.(23) one can write 2

32e

3 ee2

10.458 10

1n n

Z

EEn

I n

σ∗

∞−=

= ⋅ + ∑

&, cm2.

So, the cross-section for the fixed level can be written as follows

26 2

e, 3e

10.692 10 , cmn

I Z

E nσ ν

−= ⋅ &. (27)

Then the absorption cross-section of all energy levels can be written as follows

6 2e 3

e

10.692 10

n n

IZ h

E n hσ ν∗

∞−=

= ⋅ =∑&

232 2

3 ee2

10.458 10 , cm

1n n

Z

EEn

I n∗

∞−=

= ⋅ + ∑

&, (28)

where 2

15e ee e0.175 10

2E T−= = ⋅m v

.

For the hydrogen atom 1221.79 10I −= ⋅& erg.

Then 2

He, 3

e

10.086n

Z

n Tσ ν= ⋅ , cm2 (29)

4. The cross-section of the bound-free absorption

We will use the following assumptions:1. The spectral density of radiation is defined by the Planck formula with electronic temperature

( )3

, 3e

8 1

exp 1bh

Uh kTc

νπ ν

ν= −2. The number of the electron capture acts with emissivity of light quantums is compensated by the same number of the photoionization processes with absorption of the light quantum.

Let us consider a principle of detailed energy balance in the following form:

( ) ( )e,i e e e e e, ,d d 1b h kT

n n n

U cN N f N e

hν ν νσ ν σν

−= −v v v . (30)

The left part of Eq.(30) sets number of electron capture acts per 1 s in a volume 1 cm3 with emissivity of light quantum with frequency ( )dν ν ν÷ + . These electrons

have velocities ( )e e ed÷ +v v v , and each electron is

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captured from a free condition to the level number n. The right part of Eq.(30) sets the appropriate quantity of the electron detachment acts from the level n with corresponding absorption of a light quantum. Here ,nνσ is

the spectral cross-section of the absorption for the energy level n.

In the case of two-temperature plasma there is not necessity to establish connection between concentrations

i e,N N and eN by means of the Saha equation, therefore

we will use the following form

( ) ( )e

i e, e e e e,

,

1 1d

d1n nh kT

n b

N Nf

N U eν νν

νσ σν−= ⋅−h

v v vc

. (31)

Let us substitute into Eq.(30) the following formulas

( )3 2 2

2e e ee e e e

e e

d 4 exp d2 2

m mf

kT kTπ π

= −

vv v v v ,

( )3

, 3e

8 1

exp 1bh

Uh kTc

νπ ν

ν= − .

Then

( )e e2

i e, 2

11

d8h kT h kT

nn

N N ce e

Nν ννσ νπν

−= − ×

( )e1

1 h kTe ν −−× − ×

2e e e

3 223e

e e e,e

4 d2

m kTn

me

kTπ σπ

− × ⋅

vv v .

Exponential coefficients can be transformed as follows

2 2e e e e

2e e e e

1 1 1

2 2

m mh Ih

kT kT kT kT n

ν ν − ⋅ = − = ⋅ &v v

,

since 2

e e2 2

mIh

nν+ =

& v.

Then 2

e2

i e, 2

1

d8I n kT

nn

N N ce

Nνσ νπν= ×&

3 23ee e e,

e

4 d2 n

m

kTπ σπ

× ⋅

v v

But e ee

dd

h

m

ν=v v , since 2

e e22

m Ih

nν= − &v

Then

2e

3 222i e e

, e e,2ee

428

I n kTn n

n

N N mc he

N kTmνσ π σππν

= ⋅ ⋅

&v

But2

e2 6 2

e, 2 3 2 3e e e

32 2

3 3I n kT

ne IZ

eh m c m n

πσ ν= ⋅ ⋅ &&v

Then3 222

i e e e e, 2 2

ee

24

2 28n

n

N N m mc h

N kTmνσ π ππν

⋅= ⋅ ⋅ × v

2 6

2 3 2 3e e e

32 2

3 3

e IZ

h m c m n

πν× ⋅ ⋅ &

v,

and

( ) ( )2

e2 6 2

i e, 3 2 3 2 3 33 2

e e

32 1

2 3 3

I n kTn

n

N N e IZe

N nkT hcmν

πσ νπ= ⋅ &&.

Let's designate

( )

2 625

3 2 3 2e

320.535 10

3 3 2

ea

hc k m

ππ

∗ = = ⋅ .

Then

2e

2

, i e3 3 3 2e

1 1 1I n kTn

n

Z Ia e N N

Nn Tνσ ν

∗= ⋅ ⋅ ⋅&&. (32)

The required coefficient of the bound-free absorption is defined by summation:

2e

2i e

3 3 2 3e

1 I n kTbfn n

n n n n

N NZ IN a e

T nν νκ σ ν∗ ∗

∞ ∞∗= =

= = ⋅ ⋅∑ ∑ &&. (33)

The total coefficient of the bound-free absorption together with the free-free transitions in the fields of residual ions can be written:

2e

2i e

3 3 2 3e

1 I n kT

n n

N NZ Ia e

T nνκ ν ∗

∞Σ ∗=

= ⋅ ⋅ +∑ &&

( )1 22 6

i e e e2 3e ee

4 2,

3 3

Z eg N T

m kThcm

πν

+

N N

or, taking into account the numerical meanings of the coefficients, one can write

2e

225 i e

3 3 2 3e

10.535 10 I n kT

n n

N NZ Ie

T nνκ ν ∗

∞Σ=

= ⋅ ⋅ +∑ &&

( )2

8 i ee e3 1 2

e

13.69 10 , ,

cm

Zg N T

Tν+ ⋅ N N. (34)

If instead of spectral dependence frequency to use wave number cω ν= , where c is the light velocity, than we

shall receive the final required formula

2e

26

i e3 3 2 3e

10.197 10 I n kT

n n

Z IN N e

T nνκ ω ∗

∞Σ −=

= ⋅ +∑ &&

( )2

22i e e e3 1 2

e

10.137 10 , ,

cm

ZN N g N T

Tω−+ ⋅ (35)

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5. Absorption coefficients in atomic lines

The oscillators strengths of atomic lines of the hydrogen plasma are approximately determined from the formula:

( ) ( )2 3 3 32 2

64 1

3 32mn

gf

m m nI m I nπ= −

, (36)

where: g ≅ 1 is the Gaunt factor, taking into account the quantum-mechanical amendments, m, n are the principal quantum numbers of the lower and upper energy states.

Table 1 Parameters of the hydrogen atomic lines at m → n transitions

m no

11215 A 0.1215 82304.5 cmLα −= = µ = 1 2

o11026 A 0.1026 97465.9 cmLβ −= = µ = 1 3

o1972 A 0.0972 102880.7 cmLγ −= = µ = 1 4

o1949 A 0.0949 105374.1 cmLδ −= = µ = 1 5

o1937 A 0.0937 106724.0 cmLε −= = µ = 1 6

o16563 A 0.6563 15236.9 cmHα −= = µ = 2 3

o14861 A 0.4861 20572.0 cmHβ −= = µ = 2 4

o14340 A 0.4340 23041.5 cmHγ −= = µ = 2 5

o14101 A 0.4101 23384.0 cmHδ −= = µ = 2 6

o13970 A 0.3970 25189.0 cmHε −= = µ = 2 7

o1

4 18751 A 1.8751 5333.0 cmP −= = µ = 3 4

o1

5 12818 A 1.2818 7801.5 cmP −= = µ = 3 5

o1

6 10938 A 1.0938 9142.4 cmP −= = µ = 3 6

o1

7 10049 A 1.0049 9951.2 cmP −= = µ = 3 7

The broadening of the hydrogen lines in the majority of practically important cases is defined by the quasistatic broadening of ions and shock broadening of electrons. The half-width, caused by action of ions can be appreciated from the Holtsmark theory [8]:

( ) 2 310 2 2H,i i0.33 10 n m Nγ −≅ ⋅ − , cm−1. (37)

The shock broadening of lines of hydrogen-like atoms by electrons under the simplified theory [8] is estimated from the formula:

( )( )H,e 220 e

16

9 2z c h mγ π π≅ ×

( ) ( )e

5 5 1 3 5 2e e e0.33 ln

N

v m n v N n× ≅ + +

( )( ) ( )

-16 5 5e

2 1 2 5 1 2 1 3 5 2e

0.4 10

ln 6.21 10 0.33

N m n

z T T N n

⋅ +≅ ⋅ + (38)

where: z is the charge of nucleus, Te is the electronic temperature in К. In details with the theory of the broadening of hydrogen lines it is possible to acquaint in Ref.8. The typical nomenclature of hydrogen lines, taken into account in calculations of radiation transfer is shown in Tables 1,2.

Table 2 Parameters of lower levels of the hydrogen atomic lines

M J 2 1g J= + gΣ mE

1 1 2 2 2 0

2 1 2 2

1 2 2 8 82258.

121 4

3 1 2 2

1 2 2 14 97492.

121 4

122 6

In summary of the considerations of calculation methods for determination of atomic lines parameters we shall note, that groups of lines, engaging close to photo-ionization thresholds effectively may be taken into account by prolongation of thresholds in the long-wave party. It is may be substantiated by a partial non-realization of upper exited levels in plasma and strong overlapping of such lines.

At simultaneous Doppler and Stark broadening the structure of a line is described by the Voigt function:

( )( )

( )( )

2

1 2 22

expd

ln 2D

yx y

x y

ακ πγ π α∞

−∞

−=

+ −∫ , (39)

( ) ( )( )2 1 20ln 2 ln 2

,L

D D

xγ ω ωα γ γ

−= = ,

where 0ω is the wavenumber of center of the line. Instead

of integral (39) it appear convenient to use rather simple approximation of the Voigt function. If to enter

designations ( )0 ,v L vη ω ω γ ξ γ γ= − = ( vγ is the half-

width of a line with the Voigt contour), then [9]:

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( )( ) ( ) ( )1 2 2

,ln 2 1 exp ln 2v

ακ η ξ γ π ξ η= +− −

( )( )

2

1

1vz

αξ ξαξπγ η

−+ − +

, (40)

( )( )

1 22 2

1 22 2

4 1 20.05

2 4

D L D Lv

L L D

γ γ γ γγγ γ γ

+ + −= ++ +

,

( ) ( )1,5 ln 2 1vz πγ ξ= + + ×

( ) ( ) 12 2 40.66exp 0.4 40 5.5η η η − × − − − + .

Use of the formulas (40) allows to calculate the profile of the Voigt line with accuracy 3%, that quite enough for practical purposes.

The total absorption coefficient in a spectral range ω∆with atomic lines is determined by the formula:

( )0 ,N

ci i

iω ωκ κ κ ω ω∆= + ∑ , (41)

where: cωκ∆ is the background absorption coefficient in a

quasicontinuous spectrum, ( )0 ,i iκ ω ω is the spectral

absorption coefficient, caused by the i-th line located at 0iω , N is the number of lines, getting in ω∆ .

6. Numerical simulation results

This section contains calculated data for the two-temperature hydrogen data at pressure p = 1 atm. The computing code used for these calculations was developed on the basis of the quasiclassical theory of the free-free and bound-free quantum transitions, and also on the theory of radiative quantum transitions in atoms and molecules [5]. Initial data for these calculations (volume concentrations of the heavy particles H, H+, H2 and electrons) were prepared in the Centro di Studio per la Chimica dei Plasmi del CNR, Bari, Italy [1].

Figures 2−5 show these calculated data. Each presented figure contains all necessary information: temperatures of the heavy particles and electrons, and also volume concentrations of the particles ( i ix p p= , where

, ip p are the total and partial pressure).

It should be stressed that different thermodynamic models were used for calculation of the species concentrations. Figures with indexes b, c and d illustrate effect of the thermodynamic models on the spectral optical properties. In the first case (b, c) the equilibrium composition was calculated by free energy minimization, and in the second case (d) the equilibrium composition was calculated by entropy maximization [1].

Acknowlegments

This work has been supported by Agenzia Spaziale Italiana (contract I/R/038/01) and Russian Foundation of Basic Research (project No. 02-01-00917).

References

1. Capitelli, M., Colonna, G., Gorse, C., Minelli, P., Pagano,D., Giordano, D., “Thermodynamic and Transport Properties of Two Temperature H2 Plasmas,” AIAA 2001-3018, 35th AIAA Thermophysics Conference, June 11−14, 2001, Anaheim, CA

2. Kramers, H.A., Quantum Mechanics, North-Holland Publishing Co., Amsterdam. Translated by D. ter Haar, 1958

3. Unsold, A., Ann. Phys., 1938, Vol.33, p.6074. Armstrong, B.H., Nicholls, R., Emission, Absorption

and Transfer of Radiation in Heated Atmospheres. Pergamon Press, Oxford, 1972

5. Surzhikov, S.T., ”Computing System for Mathematical Simulation of Selective Radiation Transfer,” AIAA 2000-2369, 34th Thermophysics Conference, June 19-22, 2000, Denver, CO

6. Zeldovich, Ya.B., Raizer, Yu.P., Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, “Nauka”, Moscow, 1966 (in Russian)

7. Landau, L.D., Lifshitc, E.M., Theory of Field, “Nauka”, Moscow, 1988 (in Russian)

8. Sobelman, I.I., Atomic Spectrum Theory, Moscow, “Phys.-Math. Lit. State Publisher”, 1963 (in Russian)

9. Matveev, V.S., Approximation Formulas for Profiles of Absorption Coefficients and Equivalent Widths of Voigt’s Lines, Journal of Applied Spectroscopy, 1972, Vol.16, No.2, P.228 (in Russian).

AIAA 2002-3222


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25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-5

10-4

10-3

10-2

10-1

100

101

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104

Absorption coefficient, 1/cm

T = .500E+04Te = .500E+04P = .100E+01ABp = .347E-04Nom = 10000E- = .339E-05H+ = .339E-05H2 = .193E-01H = .993E+00

Fig.2,a Spectral absorption coefficient of low temperature hydrogen plasma at p=1 atm

25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-3

10-2

10-1

100

101

102

103

104



Fig.2,b Spectral absorption coefficient of low temperature hydrogen plasma at p=1 atm

25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-2

10-1

100

101

102

103

104



Fig.2,c Spectral absorption coefficient of low temperature hydrogen plasma at p=1 atm

25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-2

10-1

100

101

102

103



Fig.2,d Spectral absorption coefficient of low temperature hydrogen plasma at p=1 atm

AIAA 2002-3222


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25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-2

10-1

100

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103


T = .100E+05Te = .100E+05P = .100E+01ABp = .103E+00Nom = 10000E- = .213E-01H+ = .213E-01H2 = .554E-04H = .970E+00


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-2

10-1

100

101

102


T = .100E+05Te = .150E+05P = .100E+01ABp = .584E-01Nom = 10000E- = .390E+00H+ = .260E+00H2 = .775E-05H = .363E+00


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-3

10-2

10-1

100

101


T = .100E+05Te = .200E+05P = .100E+01ABp = .230E-01Nom = 10000E- = .674E+00H+ = .337E+00H2 = .139E-09H = .154E-02


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-2

10-1

100

101




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10-2

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T = .150E+05Te = .150E+05P = .100E+01ABp = .310E+00Nom = 10000E- = .309E+00H+ = .309E+00H2 = .115E-05H = .394E+00


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-3

10-2

10-1

100

101




25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-4

10-3

10-2

10-1

100


T = .150E+05Te = .300E+05P = .100E+01ABp = .294E-02Nom = 10000E- = .675E+00H+ = .338E+00H = .108E-05


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-3

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10-1

100




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25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

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25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

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25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-5

10-4

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10-1

100


T = .200E+05Te = .400E+05P = .100E+01ABp = .678E-03Nom = 10000E- = .675E+00H+ = .337E+00H = .232E-07


25000 50000 75000 100000 125000 150000Wavenumber, 1/cm

10-4

10-3

10-2

10-1

100




Documents

[American Institute of Aeronautics and Astronautics 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference - St. Louis, Missouri (24 June 2002 - 26 June 2002)] 8th AIAA/ASME